101. A Dynkin Game on Assets with Incomplete Information on the Return
- Author
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Tiziano De Angelis, Fabien Gensbittel, Stéphane Villeneuve, Università degli studi di Torino = University of Turin (UNITO), Toulouse School of Economics (TSE), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), and Università degli studi di Torino (UNITO)
- Subjects
TheoryofComputation_MISCELLANEOUS ,0209 industrial biotechnology ,Computer Science::Computer Science and Game Theory ,General Mathematics ,Boundary (topology) ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Nash equilibrium ,Set (abstract data type) ,FOS: Economics and business ,010104 statistics & probability ,symbols.namesake ,Free boundaries ,020901 industrial engineering & automation ,Complete information ,Bellman equation ,FOS: Mathematics ,0101 mathematics ,B- ECONOMIE ET FINANCE ,Mathematics - Optimization and Control ,Mathematics ,Rate of return ,Probability (math.PR) ,Incomplete information ,Zero-sum games ,Hitting time ,ComputingMilieux_PERSONALCOMPUTING ,TheoryofComputation_GENERAL ,[SHS.ECO]Humanities and Social Sciences/Economics and Finance ,Mathematical Finance (q-fin.MF) ,Computer Science Applications ,Zero-sum game ,Optimization and Control (math.OC) ,Quantitative Finance - Mathematical Finance ,symbols ,Mathematical economics ,Mathematics - Probability - Abstract
This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a bi-dimensional diffusion $(X,Y)$. Then we characterize the existence of a Nash equilibrium in pure strategies in which each player stops at the hitting time of $(X,Y)$ to a set with moving boundary. A detailed description of the stopping sets for the two players is provided along with global $C^1$ regularity of the value function., 37 pages, 1 figure, new Section 8 added; keywords: Zero-sum games; Nash equilibrium; incomplete information; free boundaries
- Published
- 2021